Laser Doppler Vibrometry is a well established experimental technique for non-contact measurements of vibrations. With the measurement object fixed in space, 1D or 3D vibration information of single points or of complex measurement grids can be obtained widely independent of the properties of the object. Under operating condition, however, numerous objects, especially car components, are either rotating or moving in space. Therefore a flexible tracking system has been developed for measuring a whole grid of measurement points on arbitrarily moving structures with a focus on rotating objects. The well established software of a commercial Scanning Laser Doppler Vibrometer (SLDV) with all its features like definition of the measurement grid, data acquisition, analysis or data presentation is used to scan the grid on the object in a well-defined starting position. The movement of the actual measurement point is continuously calculated by a separate tracking controller. During a preliminary teaching phase, the tracking algorithm calculates the traces of selected measurement points depending on a position signal of the object. In the measurement phase, the tracking controller obtains the coordinates of the actual measurement point as defined in the starting position from the scanning vibrometer. The trace of this measurement point is calculated from approximate trajectories of the teaching phase and the actual position of the measurement point is then continuously calculated according to the object position. Applications of the system for the measurement of the deflection shape of different rotating fans are presented.